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- W4309223605 abstract "T. Harima and J. Watanabe studied the Lefschetz properties of free extension Artinian algebras C over a base A with fiber B. The free extensions are deformations of the usual tensor product; when C is also Gorenstein, so are A and B, and it is natural to ask for the relation among the Macaulay dual generators for the algebras. Writing a dual generator F for C as a homogeneous “polynomial” in T and the dual variables for B, and given the dual generator for B, we give sufficient conditions on F that ensure that C is a free extension of A=k[t]∕(tn) with fiber B. We give examples exploring the sharpness of the statements. We also consider a special set of coinvariant algebras C which are free extensions of A, but which do not satisfy the sufficient conditions of our main result." @default.
- W4309223605 created "2022-11-24" @default.
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- W4309223605 date "2022-12-01" @default.
- W4309223605 modified "2023-10-16" @default.
- W4309223605 title "Artinian Gorenstein algebras that are free extensions over k[t]/(tn), and Macaulay duality" @default.
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- W4309223605 doi "https://doi.org/10.1216/jca.2022.14.553" @default.
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